My husbands i3 just stopped charging in its usual outlet in the garage last night. The outlet still gets power, but when we plug the charging unit in, "power fault" lights up solid red. We thought something was wrong with the charging unit itself, but after messing around with it for a while, I learned that it works if I plug it into the bathroom GFCI outlet, running an extension cord through the window... not ideal. Obviously I can get a GFCI in the garage, but that will take a few days.

High loads like the EVSE over time can cause a builder's grade receptacle lose tension on the contacts, and the heating/cooling of the wires at the terminals can cause them to loosen up. It might be just that the screw clamp on the receptacle is (are) loose. It does not need to be a GFCI device (the EVSE essentially has that function in it to protect you when charging), but current code does require it on new construction in a garage, so for use with other things, prudent.

But, first thing that I would do is replace the receptacle with a commercial grade unit. That will probably resolve your problem. If your extension cord is not of sufficient gauge (depending on the length, at least 14g wire, and if longer, a 12g one would be better), you will have issues long-term, too.

It's fairly common for there to be more than one receptacle on a branch circuit, and for it to be fed through from another one. ALl it takes is one loose connection. If there was one, you likely have another. All it takes is one. The unit MUST see a ground and reliable connections for hot and neutral to work properly. A GFCI has nothing to do with it.

First, you should have a GFCI in the garage. Note that GFCI outlets can have other GFCI outlets daisy chained off them, making every outlet on the chain protected against ground faults. That is, you may already have a GFCI in-line with the non-GFCI outlet. There is no need for multiple serially wired GFCI outlets.

Second, there is nothing about a GFCI outlet that will make an EVSI work where it would not work on a PROPERLY WIRED non-GFCI outlet. If anything, the GFCI circuitry could make the EVSE work less reliably. The GFCI protects against leakage current past the outlet, and also will not work if it is not properly wired itself. There should be no leakage currents due to the EVSE, unless, for example, water is getting in somewhere between the car and the outlet, providing an electrical path to ground to one or both of the hot wires.

My guess is that there are wiring issues somewhere between the outlet and the main panel. Most probably, the outlet itself. Could also be other things plugged into the same circuit that is causing issues with the EVSE.